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Module Digit DP

Digit DP

**Frequency: 2/10** Digit DP problems usually ask you to count the number of numbers in a range satisfying some certain conditions. The problem statements for Digit DP typically have clear indications that the technique should be used. Hence, in a contest, it is essential to manage your time wisely when attempting Digit DP problems, as problem setters intentionally make them challenging to code. Tip: When solving problems, consider using a different number base if necessary, such as base-2, to optimize time complexity.

Resources

- [Scaler: Digit DP](https://www.scaler.com/topics/data-structures/digit-dp/)

Problems

Unlucky number 313 / 324 1300
Digit Sum 342 / 353 1400
Divisible 225 / 270 1400
Prime digit sum 221 / 238 1500
Non-palindrome number 178 / 200 1500
Yet another XOR problem 116 / 127 1600
Taboo substring 74 / 96 1700
Balanced number 41 / 47 1700
Equation 56 / 70 2100
Beautiful number 47 / 79 2100
Constructing numbers 25 / 33 2200

Data structure

  • Sweep Line
  • Introduction to Trie
  • Square root decomposition

Tree

  • Rerooting
  • Small-to-large
  • Heavy-light decomposition

Graph

  • Strongly connect component
  • Articulation point and bridge
  • Bipartite Matching

Dynamic Programming

  • Digit DP
  • Matrix multiplication

Hashing

  • Hash a set

Others

  • Divide and conquer

Geometry

  • Geometry

Binary search

  • Parallel binary search

Others

  • Additional Problems (Level 5)